Question

It is $165\mathrm{cm}$from your eyes to your toes. You're standing$200\mathrm{cm}$ in front of a tall mirror. How far is it from your eyes to the image of your toes?

Short answer

Distance from eyes to the image of toes,$d=433mm$

Step-by-step solution

Explanation by image

The incident and reflected rays are within the same plane and parallel to the surface.

The angle of incidence and reflection are the identical.${\theta }_i={\theta }_r$

Find Distance using given values

$165$cm separates your eyes from your toes.

There is $200$cm between you and the mirror.

FIGURE shows a one ray from a human toes reflecting from the mirror to the person's eyes. the reflected travels along a line that passes through a degree on the backside of the mirror, according the law of reflection, ${\theta }_i={\theta }_r$therefore, the space between the person's toe and therefore the mirror is that the same because the distance between the mirror and also the toe's image behind the mirror

Using Pythagorean theorem,

$d=\sqrt{(165\mathrm{cm}{)}^2+(400\mathrm{cm}{)}^2}$

$d=433\mathrm{cm}$